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 A066389 Number of 2-generated groups of order n: groups that have a generating set of size <=2, i.e., are cyclic or of the form . 3
 1, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 5, 1, 2, 1, 9, 1, 4, 1, 5, 2, 2, 1, 13, 2, 2, 4, 4, 1, 4, 1, 20, 1, 2, 1, 12, 1, 2, 2, 12, 1, 6, 1, 4, 2, 2, 1, 35, 2, 4, 1, 5, 1, 10, 2, 11, 2, 2, 1, 13, 1, 2, 4, 54, 1, 4, 1, 5, 1, 4, 1, 37, 1, 2, 3, 4, 1, 6, 1, 35, 10, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Eric M. Schmidt, Table of n, a(n) for n = 1..1023 PROG (GAP) IsTwoGenerated := function(G) if IsSolvableGroup(G) then return (Length(MinimalGeneratingSet(G)) <= 2); fi; return ForAny(List(ConjugacyClasses(G), Representative), g->ForAny(G, h->Size(Group(g, h)) = Size(G))); end; A066389 := function(n) local count, i; count := 0; for i in [1..NumberSmallGroups(n)] do if IsTwoGenerated(SmallGroup(n, i)) then count := count + 1; fi; od; return count; end; # Eric M. Schmidt, May 02 2013; shortened by Eric M. Schmidt, May 20 2013 CROSSREFS Cf. A000001. Sequence in context: A072342 A257089 A234541 * A077191 A050363 A166974 Adjacent sequences:  A066386 A066387 A066388 * A066390 A066391 A066392 KEYWORD nonn,nice AUTHOR Sharon Sela (sharonsela(AT)hotmail.com), Dec 23 2001 EXTENSIONS More terms from Reiner Martin (reinermartin(AT)hotmail.com), Dec 29 2001 More terms from Eric M. Schmidt, May 02 2013 STATUS approved

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